Method of mining



March 19, 1946. P, B. BUCKY 2,396,678

METHOD "oF MINING FiledlJan, 15, 1941- a-sheet's-sheet 1 Roc/f "o \fw "A 1 Reck "e V ons src Pc ons cR A oke [Si Bo-r-T'M R@ ATTORNEY March 19,1946. P. B, BLJCKY l v2,396,678

METHOD 0F MINING INVENFOR. PH/L/P B. .Bz/CKV HT'T'ORNEYl Patented Mar. 19, 1946 UNITED STATES PATENT OFFICIE METHOD F MINING Philip B. Bucky, Larchmont, N. Y.

Application January 13, 1941, Serial No. 374,140

3 Claims.

The present invention relates to a method of mining and is specifically directed to a method of designing `underground structures which Will be safe and insure economical exploitation of ore bodies.

It has been Well established that many engineering problems due to their inherent complexity, cannot be solved mathematically. This has been particularly true of mining problems due to the irregularity of nature. In the present state of knowledge, the dimensions and shapes of mine structures have been determined empirically by field experience and only in rare cases have structural calculations been attempted. Neither of these methods, however,

is based on sufficiently scientific principles to place the design of mine structures on a sound basis. Lack of data has prevented economic mining of ore bodies on one hand, and on the other hand, has been the cause of failures of mine structures with ensuing loss of life, cavein of mines, landslides and subsidence of city streets and buildings. At the beginning of the last decade I proposed another method lfol' solving certain problems arising in the design of mine structures. This method was predicated on the use of small scale models of mine structures. The models Were made in every respect from the same materials as their prototypes and were prepared in accordance with principles of similitude which could be established by the laws of mechanics. The procedure involved studying the behavior of the scale models thus prepared, under simulated loading conditions.

In applying this method, I discovered the principle that if in the scale model of a mine structure, the pull of gravity on eachportion of the model could be increased in the same proportion as the linear scale of the model was decreased, then, the unit stresses at corresponding points in the model and prototype would be the same, and the displacement or deflection of any point in the model would represent to scale the displacement of the corresponding point in the prototype. The increase in gravity Was obtained by substituting a centrifugal field for the gravitational field. This was accomplished by placing the model in a suitably designed centrifuge and rotating the centrifuge with the model mounted therein,-at a speed calculated to produce the desired multiple of gravity. While the radial centrifugal eld was not uniform in either amount or direction, for practical purposes it could be assumed to be approximately uniform if the radius of the centrifuge was large compared to the dimensions of the model. Establishment of the foregoing principle has made possible the study through scale models,` of the behavior of projects of 'large magnitude stressed within and beyond the elastic limit. From the data obtained from the study of the behavior of these small scale models in the centrifuge, I have been able to determine the proper shape and dimensions of underground openings, the proper shapes and dimensions of the geological support required as pillars to support mine roofs; the proper shape, dimensions and spacing of any additional artical support that may be necessary in order that no part of the geologic structure shall fail; the length of working face; the amount that this face may be Worked back at a time; and the amountand disposition of artificial support which shall allow for the safe ingress and egress of machinery and men between the face and the artifical support and at the same timeshall cause the failure of the roof and overlying material to be such as not to interfere with the Working at the face;

However, when the geologic section of amine becomes complex so that the roof of a mine structure comprises several superimposed layers of different rock formation each of different thicknessand physical properties, the preparation of the scale model becomes correspondingly complex. Further, the useof scale models prepared from the same materials as their prototypes does not furnish any direct information as to the stresses, their direction'and distribution in a mine structure. For the-design of pillars and the placing of openings with respect to other portions of a mine, these data are desirable. Also, heretofore, the scale model principle has had limited application to the solution of mining problems. The designing of mine structures for insuring block caving, for delaying the failure of mine structures for a given period of time, and the like, by prior art methods has left much to be desired.

I have discovered that simplied models of complex geologic sections may be vprepared Which nevertheless -will furnish, when tested, adequate data for the design of mine structures. I have also ascertained that information as to the stresses, their direction and distribution in mine structures may be obtained through the use of models prepared from photo-elastic material. I have further found thatl the time'a mine structure will stand can be predeterminedvand may be ascertained from the testing of a scale model. I have still further found that the scale model principle is applicable to the investigation of other mining problems, the solution Y of which heretofore was inadequate for practical purposes.

It is an object of the present invention to provide a novel procedure in the model method which takes into account the loading factor of the various rock beds of multi-strata geologic sections. f

It is another object of the present invention to provide a novel procedure in the 'model method which is characterized by the use of models prepared from photo-elastic materials which may be investigated in accordance with photo-elastic methods.

It is also an object of the present invention to' in conunction with the accompanying drawings in which:

Figs. l and 2 are representations of vgeological sections of .mines showing mine roofs comprising several rock beds of varying thicknesses.

5. Ascertaining the rock beds which must be represented in the scale model.

6. Determining the maximum or desirable dimensions of the model.

7. Constructing the model.

8. Testing the model in a suitable dynamic eld.

9. Obtaining data and observing results.

10. Designing the mine structure from the aforesaid test results and data.

1l. Conducting mining operations in conform- Vity with the design based upon thetest data and results to produce the predetermined mine structure.

In actual practice, those skilled in the art will understand that under certain conditions some vof the aforementioned steps may be eliminated or Fig. 3 is a diagram showing the stresses at a point AO of a loaded structure.

Fig. 4 is a representation of a geological section of a mine showing a mine roof comprising several rock beds of varying thicknesses and Va pillar partially supporting the mine roof and overlying material.

Fig. 5 is a curve showing the relation between span and time of failure in the field.

Fig. 6 is a curve showing the relation between model ratio and time of failure in both the model and the prototype; Y

Broadly stated, the invention providesV anew andV improved method of designingi mine structures which eliminates the empirical approximations ordinarily involved therein and as a corollary thereto, permits safer and at the same time more economical exploitation of ore-bodies. In

. general, my improved method involves studying termined results.

'In accordance with the present invention, the method embraces the following steps:

1. Determining or ascertaining theV geologic section of a mine property.

V2. Obtaining field samples from the mine property.V Y

3.V Determining the properties of the materials of the samples, e. g., the modulus of elasticity,

the tensile strength, the compressive strength and/or the shear strength of the materials.

4. Determining theY loading factorgof the rock beds making up the mine roof.

combined. Thus, steps l and 2 may be combined and the geologic section of the mine property ascertained from the field samples or-from prior knowledge of the mine property, etc.

In carrying the present invention into practice, the geologic structure and the section of a mine may be determined by procedures well known to geologists and to mining engineers. Boreholes and cores obtained from drilling operations give an indication of how the rock strata lie relative to one another and of the thickness of each layer. In addition, considerable information may be obtained from studies of the surface geology and from geologic maps and sections prepared by the United States Geological Survey and by the Various states geological surveys. This information should include data relative to materials underneath the-oreY body and should comprise at least data on any soft layers having plastic properties which are adjacent to the ore body. Field samples of the various rock strata and of the ore body may be obtained from outcrops, borings,

Vor openings of various kinds passing through geologic beds. The dimensions of the samples will depend upon the dimensions of the testing device, e. g., the centrifuge, the ability to Work the material to a given shape and to certain dimensions, and the ultimate accuracy desired.

yThe samples must be of such dimensions as to permit both structural and model tests and generally are larger than the usual samples taken heretofore.

To determine the loading factor of beds over ore bodies, it is important to ascertain whether the overlying rock beds will or will not have a tendency to load the roof of a mine. The load of a'rock bed on the one beneath it bears a relationship to the tendency of the several rock beds to deect or sag over a given span; thus, if the lower bed defiects more than Vthe upper one, it cannot be loaded by the upper one, While if it deflects to a lower degree, it will be loaded by the upper one. The calculated deflections relative or absolute, of all the rock beds of a geologic section are therefore indications of Whether certain rock beds or groups of rock beds will load each other or not and'therefore whether their presence in a model is necessary. These data are also the basis for determining the amount of artificial support necessary for mine roofs, i. e., the load that an artificial support must be designed for. In applying the foregoing, samples from each bed are cut to uniform dimensions. The samples are then weighed and the density (d) of each sample in pounds per cubic inch or foot is determined. Each sample is then placed in a loading device as a beam and a light concentrated load (W) is Aapplied thereto. The deflection (A) is measured with any suitable measuring device.

From mechanics in which W--the concentrated load E=the modulus of elasticity I=the moment of inertia 'L=the length of span and since all the beams of the model .have the same dimensions and are loaded equally,

Hence Formula 1 may be Written thus:

Where the load is uniform, Formula l may be written thus:

=a constant, K

Afr-o2 in which dzdensity D=thickness of the bed rock K=another constant Au=the deflection of a uniformly loaded beam.

In view of what has been stated already, Au or the deflection of a uniformly loaded rock bed may be taken as the loading factor (F) of the rock bed, or

Kd :rm (3) The loading factor of a group of rock beds (FG) which load one another, may be represented by the following formula:

Hence, the bending effect of a group of rock beds over an opening or support may be obtained from a single bed whose loading factor is obtained from the loading factors and the thicknesses of individual rock beds making up the group and whose field thickness is obtained from Formula 2 above. In general, I have found that a rock bed with a greater loading factor will not be loaded by a rock bed with a smaller loading factor above it, but that it will load a rock bed with a lesser loading 'factor beneath it.

It is therefore apparent, that if the loading factor of the rock bed is taken into consideration, parts of a model may be scalar and parts nonscalar and of different material. The eleots of the strength of the bond between rock beds should be considered particularly if a thicker rock bed overlies a thinner one and the strength of the bond is large, thereby decreasing the loading factor of the thinner rock bed and increasing the loading factor of the thicker rock bed. While the strength of the bond may be of par- In vvievv ofthe foregoing, it appears clear that While a scale'model can be prepared so that every detail lwill be rsimilar to its prototype, a model comprising only a portion of the Aprototype may be all that is necessary. By Way of illustration and referring to Fig. 1, if rock beds A= 1 ft. in thickness y B: 5 ft. in thickness C=20 ft. in thickness D=50 ft. in thickness then DA: 1 DB= 5 Dc=20 If the beds are of the same rock and if E=ll6, d=100 lbs./ft.3, and lc=105, then from Formula 3 above, the loading factor of rock bed MFA) is equal to K'z 1o' 1co Umm-W40 similarly Hence, applying the general principle, bed A will not be loaded by beds B, C and D. The loading factor (Fo) of the group of rock beds may be obtained by substituting in Formula 4 as follows:

Bending effects of a group of beds over an open ing or support may therefore be obtained from a single bed whose loading factor FG=0.057 and whose field thickness maybe obtained by substituting in Formula 3, as follows in which E is the modulus of elasticity and d is the density of the rock which goes into the model:

whence, solving for D, D=42 ft.

Any rock may be used in constructing the model, preferably rock from one of the rock beds in the geologic section. The thickness for model purposes will be 42 ft. divided by the model ratio decided upon. Thus, in view of the foregoing, for the conditions shown in Fig. l, the roof bed A will not be loaded by any of the others, and hence, a scale model including A alone and representing A alone is all that is necessary for the determination of the immediate roof behavior. If the geologic section is as represented in Fig. 2, then by applying the general principle, it will be seen that rock bed A will be loaded by the overlying rock beds, B, C and D, and therefore, all the rock beds should be included and represented in the model, or a simplified model may be pre pared which will include one rock bed onli Which will represent a thickness of about 42 ft. as indicated in the foregoing illustrative A example. Thus, the application of the loa-dini:

ticular importance in many cases, it may be included in the scale model and its effect on the loading factor of a bed or combination of beds thereby observed and determined.

models, and the methods of testing themodels in the centrifuge are procedures Well known to the art. The apparatus employed and the procedures involved have been fully described in the following articles:

American Institute of Mining & Metallurgical Engineers; T. P; 425 (1931);

Trans. American Institute of Mining 8: Metallurgical Engineers vol. 109 (1934);

American Institute of Mining & Metallurgical Engineers, T. P. 529 (1934);

Engineering & Mining Journal, volume 136 April 1935, page 178;

American Institute of Mining 8: Metallurgical Engineers, T. P. 946 (1938) American Institute of Mining & Metallurgical Engineers, T. P. 1020?' (1939).

To obtain data as to stresses, their direction and distribution inamine structure, in order that information may be obtained which will permit the design of pillars and the scientific placing of openings with respect to other portions of a mine; models may be constructed of materials different from their prototype and speciiically of, isotropic transparent materials such as glass, Bakelite or other synthetic materials having these properties.

The photoelastic method of stress measurement determines the stress distribution in a twodimensional model by optical 'means. This method utilizes the experimental fact that when a piece of isotropic transparent material is stressed and viewed in polarizedlight.- pictures are produced which indicate by their color bands of light or fringes, the magnitude of the stresses,' their direction and their distribution. The stress at any point O of a structure as shown in Fig. 3 may be resolved into two components called principal stresses,.P and Q, each a pure tension or compression, at right angles to each other. fully identify the stress, the values of P and Q and of angle p must be known. Photoelastic methods of stress analysis are broadly old and well known photoelastic apparatus provide means for determining the values of P-Q, the principal stress diierence or twice the maximum shear stress at O; of Pfl-Q the principal stress sum at O, and of angle qb. Having two simultaneous equations with two unknowns P and Q, their Values may be determined by algebraic or graphical means. The pictures obtained by photoelastic methods show fringes or'contour lines through points of equal maximum shear stresses (P-Q) .l These lines are called isochromatics. The value of the stress of each fringe is obtained experimentally and by counting the fringes, the maximum shear stress at any point may be determined. Similarly, the pictures obtained by photoelastic methods show fringes or contour lines through points oiv equal model thickness. These are (P--Q) contour lines and are called isopachics. The pictures obtained by photoelastic methods also make possible the determination of angle c. Under certain optical adjustments, it is possible to obtain pictures showing black lines or areas which blot ont the isochromatic fringes when the principal stresses are inclined at an angle c. These lines or areas are called isoclinics. Y Y

Photoelastic methods of stress analysis have already been applied to testing of models to determine the behavior of structures under gravitational load, e. g. Civil Engineering, volume 5, No. 5,'May 1935, page 287. Y These methods, of course, are only applicable for studying materials stressed within the elastic limit. However,

heretofore, photoelastic methods have not been used to solve complex problems arising in the design of mine structures.

The use of models prepared from photoelastic materials involves a few additional steps in the procedure hereinbefore set forth for the method in which models are prepared from the same materials as the prototype.

In accordance with this phase of the present invention, the photoelastic method embraces the following steps:

1. Determining or ascertaining the geologic section of a mine.

2. Obtaining field samples.

3. Determining the Properties of the materials, e. g., the modulus of elasticity, the tensile strength, the compressive strength. the density, and/or the shear strength of the materials.

4. Determining the loading factor of the rock beds making up the-mine roof.

5. Ascertaining the rock beds which must be represented in the model.

6. The determination of the density, the modulus of elasticity, the (P-Q) shear stress fringe value and the (P-l-Q) fringe value for the photoelastic material from which the photoelastic model is prepared.

7. Determining the maximum or desirable dimensions of the photoelastic model.

8. Determining the value of fringe stressin the prototype.

9. Constructing the photoelastic model.

l0. Testing the model in a suitable dynamic field such as a centrifuge.

il.V Obtaining data and observing results.

l2. Designing the mine structure from the aforesaid test results and data.

13. Conducting mining operations in conformity with the design based upon the test data and results to produce the predetermined mine structure.

In actual practice, as pointed out hereinbefcre, those skilled in the art will understand that under certain conditions some of the aforementioned steps may be eliminated or combined. In carrying this phase of the invention into practice, only the novel or additional steps need be considered, the others being either similar in every respect to those described and discused herein- Vbefore or suiiiciently well known in the art that reference to standard works on the subject is all that is necessary for a detailed discussion.

The dimensions of the photoelastic model are determined by using the following formula:

in which M. R.=the model ratio or scale Ep=the elastic modulus of prototype material Es=the elastic modulus of model material Cg=the ratio of strength of centrifugal to gravitational field dp=the density of prototype material db=the density of model Vmaterial The fringe stress values in the prototype are determined by using the following formula:

in lbs. per square inch, in which Snr-the value of one fringe or stress at a' point in the model while being tested. Y

Sp=the value in pounds per square inch of one fringe or stress at a similar point in the prototype.

By way of illustration, if Ep=106 dp=3 Et=2 105 db=1.5

and assuming that the centrifuge with the model mounted therein, is` rotated at such speed that 6 Sp 78% 390 pounds per square inch Therefore, it may be stated that the value of the shear stress inthe prototype of the material mentioned, Whose similar linear dimensionspare 1900 times that of thephotoelastic model', is 390 pounds per square inch or multiples thereof at.

all points Where. fringes appear, while the photoelastic modelv is being rotated in the centrifuge at a speed which will produce a centrifugal eld.

equivalent to '760 timesV gravity. If the No. 1 fringe stress value. is 390 pounds per square inch, then shear stress where the No. 6 fringe appears will be 6X390 or 2340 poundsv per square inch.

To obtain data which will permit the .design of mine structures which willv not fail for a pre-r determined period of time, the model method may be used to great advantage. Since, most geologic materials have properties Which. do not quite follow any law, it must follow that the material' is not perfectlyV elasticin any part of its stress range. Therefore, time effects. be-A come importantand hence, all struc-tures of this type of material will eventually collapse. I have discovered that the time required for a given event to take place in a prototype stressed beyond the elastic. limit, is equal to the product of the model scale and the time required for the same event to take place in a small scale model. The scale model must be made in every respect of the same material as the. prototype and must be tested in a centrifuge which rotates at such a speed, that the centrifugal field strength equals the product of the model ratio times the gravitational field strength. Thus, if a scale model fails at the end of one hour in a centrifugal field whose strength is equivalent to 1000 times gravity, it represents a prototype whose similar linear dimensions are 1000 times those of the scale model and which will' fail in 1000 hours or at the end of 41.7 days.

Thus, it becomes possible to design` mine stru tures with a safety factor based on time rather than onV stress. By Way of illustration, if a stope is to beworked out within 30 days, a safety factor of 2 based on time will call for the design of a vstope which willl fail in 60- days. Therefore, the corresponding scale modelbuilt to a scale of' 1:1000 will fail while rotating in a centrifuge: at the end ofv vIn accordance with this phase of the present invention, the procedure involves the same first seven steps of the first procedure outlined hereinbefore.Y l

Y In carrying this other: phase of the invention into practice', if mine roof failure is to be' determined, several scale models of the prototypeare prepared with varying spans. A scale model having a 'span L, is placed' in the centrifuge and rotated at increasing speeds up to thexpredetermined spee'dfto givel the desired model ratio. If no failure occurs immediately on` reaching this speed', the scale model is run for at least an hour. Another' scale model with a longer span, Lr, is then teste'dand for .illustrative purposes it may be assumed to break at a speed corresponding to a modelratio of 9,90. The next scalemodel isl prepared then with 'a span equal to Yaboutr98% ofrLi andqupon testing, let us. assume that it breaks imn'iedlately` as Vsoon as' the ,centrifuge reaches a'speed' corresponding to a model ratiov of 1000'. .This span L z is carefully measured and notedgj The next scale model; isprepared with a span corresponding to about 98% of L2 andl letus assumejthat it fails 5f minutes afterl the model is brought to speed. T his procedure isirepeated with scale models withl spans Ycorrespondingv t0 about 96% of L2, about '94%` of Lz, or other variations of L2.

With the values thus obtained, a curve is obtained by plotting spans against time required for failure. A curve similar to the one shown in Fig. 5 is obtained from which the time requiredv for failure for any given span may be determined. Other modications of. this' procedure are available for determining'tinie effects. For example, a scale model may be l. Tested to failure and the model ratio determined lwith time equal to zero.

2. A similar scale model then may beV tested at a speed'so that the model ratio is 98% of the-first test and the time required for failure noted.

3. Similar scale models. then may be tested at speeds so that the model ratios are about 96% and about 94% of the first test and the time required for each failure likewise noted.

From these data another curve, as shown in Fig. 6 may be plottedY which will give the relationship between model ratio and time required for failure. Likewise, curves similar to 6 may be' plotted for any single mine roofbed= and the relationship between'time, span,l andA roof thickness'. determined. These data will permit vthe design of mines which will require a minimum of artificial support and will fail within` a given period of time after the completion of mining operations. Further, these data make possible the designing of artificial supports which upon removal will result inthe immediatefailure of the desiredstrata.. .y l

Illustrative Vbut nonflimiti'ng examples showing applications of the'procedures of the invention for the solution 0f Various mining problems are appended hereto, although it is appreciated that numerousl other applications will become apparent tothose skilled inthe art. Y

Procedures foru the determination' of the geological support and shape of the same for safe underground spans The safe span desiredy is determined by a procedure described in T. P. l529 of the American Institute of. Mining and: Metallurgical Engineers, already'referred to and/ or procedures taking into account the loading factor ofrbed's. The size of a pillar of rectangular cross section is then estimated for this span on the basis of the strength of the material making up the pillar and the load due to the spans supported by the pillar, with a safetyv factor of 1. vA model is then prepared taking into consideration the loading factor of the rockbeds with safe spans of L1 and In which are equal as shown in Fig. 4. The model is placed in a. centrifuge and is rotated at a speed calculated to give the prototype dimensions for the span. Finally, the behavior of the pillar under test is observed carefully and it is enlarged or reduced until it shows signs of failing at speeds within 5% of those calculated. The model pillar dimensions are then approximately correct, the width of the prototype pillar is calculated with a safety factor of Y4 or any other number times the lmodel width. By way of illustrative but non-limiting example, assume that the section comprises the equivalent of 3000 inches of sedimentary rock and that the weight of this rock is equal to 1 pound per square inch per foot of height. A Assume also, that uthe safe span as previously found with a safety factor of 4, is equal to 200 feet or 2400 inches and that the strength of the pillar rock=5000 pounds per square inch.

Thus, .the Vestimated .width of pillar for 200 feet or 2400 inch spans:

5000 120 inches or feet.

' A model is prepared on the basis of bringing the model in the centrifuge to a speed so that a conveniently selected model ratio of 1200 is obtained.

The model spans are therefore e 1200y or 2 inches wide.

I-Iencethe pillar of the model is equal to or 116 of an inch wide.

l The overall thickness of the model is equal to lent-.to a model ratio of 2400, the width of the' prototype pillar should be equal to Qn the other hand, if the pillar breaks at a speed equivalent to a model ratio of 600, then the width of the prototype pillar should be equal to f =`20 feet 00d 12 Y e By-fo'uowmg' this procedure, suitably safe p11- lar widths for givenspans may be designed and safe and v economical .mining` operations may be conducted in accordance therewith.

scalare P hotoelastic prooedurepfor while the roof is 1/4 of an inch thick. The model is placed into a centrifugeandis rotated at 2000 R. P. M. At this speed, ,photographs of the isochromatics and of Athe ,iso'clinics are taken.' lf this rate of rotation of the centrifuge is equivalent to a model ratio of 760,"then the centrifugal eld strength is the equivalent of 760 times gravity. If the photoelastic model represents held proto-' types which have dimensions that are 1900 times the model dimensions, the pillars of the prototype are equal to or 158 feet, and the spans to pillar centers are equal to or 475 feet. This gives open spans of 475-158:

3l7feet.V w f i Photographs of theisochromatic fringes show the shear stress distributionV in .this pillar." Assuming that the maximum number offringes is 6 at the corners, since the material for the model thickness used has a 'fringe stress value of 78 pounds persquare'inch in shear, then the stress Value at the corners of the pillars will be equal to 6x78 or 468 pounds'per square inch. v Since one fringe in the model is the equivalent'ofa stress of 390 pounds per square inch in the material of the prototype under the conditions` assumed hereinbefore, the maximum shear stress 40 at similar corners in the prototype Awill bek equal to 6X390 pounds or 2340 pounds per square inch. Assuming that the photograph `of the isochromatic fringes also shows that the shearstress over most of the pillar v`isone fringe or 78 pounds per square inch in the'model; then this is equivalent to 390 pounds per 4square inchin the prototype.

From the foregoing, it will be -apparent that if the prototype material has a maximum shear stress value equal to -an'assumed Safety factor of 5 multiplied by the maximum shear stress value, thatis to say, 5 times 2340 or 11,700 pounds per squareinch, it will not fail. Safe pillar dimensions may therefore be'determinedby this procedure, and mining operations carried out in accordance therewith. This procedure may be combined with the previous procedure and pillar dimensions obtained therefrom. f Y

Photoelastz'c procedurejor pillars f By preparing models of photoelastic materials and by, using 'in the models, pillars of different shapes, it is possible to study the stress distribution in variously shaped pillars.V Thus, the eifect of cutting the upper corners of-a pillar shows, under testing conditions in the centrifuge, that the maximum shearstress still occurs atthe upper corners of the -pillar and that in view `of the foregoing example it isequal still to -6 78 or 468 pounds per square inchin the model and 6x39() or 2340 pounds per square inch in the prototype. The stress over the lower portion of the pillar is observed to be represented by a single isochromatic fringe, that is to say, 78 pounds per square inch in the model or 390 pounds per square inch in the prototype. It is further observed that by cutting the upper corners of the pillar, the length of pillar side affected by high stress is reduced.

When the pillar sides are arched, the maximum shear stress is increased to 'l isochromatic fringes or to 7x78 or 546 pounds per square inch in the model, or to 7X390 orv 2730 poundsV per square inch in the prototype. Further, arching of the pillar causes a longer portion of the pillar side to be stressed. Isochromatic photographs, however, stili show a single fringe over the lower portion of the pillar, which means that thev stress will remain equal to 390 pounds per square inch in the prototype.

Comparison of these data shows that the better stress distribution along the sides of `a pillar occurs when the upper corners are cut out, i. e.,` the top of the pillar is made narrower than its bottom.

In accordance with thisv procedure, shapes of pillarsl may be predetermined and safe mining operation may be conducted.

Procedure for the determination of pillars that may be removed from previously worked piroperties The maximum stope span and minimum pillar dimensions that may be used are determined by the procedures already outlined. By way of illustration, let us assume that tests conducted in accordance with the foregoing show that spans of 100 feet and pillars of 50 feet are permissible in a given property. A study of the geologic-map, and underground measurements show that this property has been worked in the past on the basis of spans of 25 feet and of pillars of 50A feet. For this condition, in view of the tests, alternate pillars may be removed in mining operations.

A modification of this procedure, whereby pillars may be removed allowing the failure of the immediate roof in a mine without. affecting the surface, may also be used. For example, with a geological section as shown in Fig. 1 and with spans of 25 feet andl pillars of 25 feet, tests conducted in accordance with the foregoing showed that if the roof bed, rock bed A of Fig. 1, is allowed to cave in or is mined, then the spans of the stopes may be increased to 125 feet andthe pillars may be maintained at 25 feet. In this latter case, in view of the tests; two adjacent pillars may be mined or removed.

Photoelasiic procedure for the determinationof pillars that may be removed from previously worked properties By preparing photoelastic models of `previously worked properties and by determining maximum spans and minimum sizes and shapesof pillars in accordance with previously outlinedprocedures, pillars of previously worked properties that may be removed may be determined on the basis of the maximum stresses to be allowed. To illustrate, let us assume that the property shows stopes with spans of 25 feet and pillars of 50'feet and that the shear stress strength of the prototype material is 10,000 pounds per square inch. Assuming that by testing the photoelasticmodel, it will appear that the shear stress within pillars of 50 feet thickness and with 100-foot open spans is 1000-pounds per square inch, it'will thus be apparent that alternate pillars mayl safely be removed in mining operations without danger of exceeding thestrengthoftheremainingpillars; f

Procedure forA the determination of the amount and position of materialsA that may be removed from pillars at present standing A model' designed in accordance with a phase of the present invention on the basis of the loadingl factor of rock beds is prepared with pillars representedv according to scale. The center portions of the pillars are removed gradually until when the model is rotated in a centrifuge at a speed equivalent to its model ratio, failure of the pillars will take place. The prototype pillai` may then be mined accordingly so that the thicknessl lef-t will' be equal to 4 times (safety factor) the model ratio times the model pillar thickness thus determined. By way ofillustration, let us assume that the model scale is equal to 1:1000, and that the model pillar thickness is equal to 1.2 inches. This is the equivalent of a prototype thickness of feet.

The center of the model, pillar is removed until the walls are of an inch thick when failure occurs undertest conditions.

Therefora the walls of the pillar to be left in the eld are equal to Hence, the amount of material to be mined from the center portion of the pillar is equal to 100-66 or 34 feet.

The pillar may also have its outer portions removed and its shape changed so that failure will occur when tested at a speed equivalent to the proper modelV ratio. Accordingly, prototype pillar shapes and dimensions may be determined =33.0 feet and mining operations conducted in accordance therewith.

Photoelastic determination of the amount and position of material that may be removed from pillars at present standing A model is prepared from photoelastic material and is then tested in a centrifuge to produce isochromatic shear stress patterns. Thereafter, the model is taken out of the centrifuge and inner or outer portions of the pillar are removed and the model is again tested. This procedure is repeated several times. If it appears that the maximum shear stress does not exceed the predetermined working values, it is safe to cut and shape the pillars. Thus a procedure is available for determining the amount and position of material that may be removed from present pillars and also the most efficient pillar shape to be used in mining operations.

This procedure may be combined with the previous procedure if desired.

Procedure for the determination of the antificial support necessary in a mine A complete model is prepared in accordance with a phase of the present invention, taking into account the loading factor of rock beds. The model is then placed in a centrifuge and tested. The model is then taken out of the centrifuge, portions of the ore body are removed, and the model is tested again. This procedure is repeated until the model fails under testing. The model span is then noted. This procedure may be followed with a model in which the mine roof is represented by several rock beds. 'I'he model may be tested until successive bedsv fail. With a prototype span greater than 1/2 that found necessary by. testto make the firstv rock bed fail, ifA a. safety factor of. 4.v isl used',l articial supports or props must be provided. The load per prop may be assumed to be equal to the area ofthe roof to be supported times the weight per unit of area. The cross section of the prop will be equal to the prop 'span weight divided by the unit load allowed for the material ofthe prop. Assuming a value of 1000 pounds per square inch for timber, the cross section of the prop will be equal to the load per prop divided by 1000.

By way of illustrative but non-limiting example, assume the mine roof thickness to be equal to feet. Assume further, that the span desired is equal to 60 feet. Let us assume, also, that the span for the failure of the iirst bed has been found by test to be equal to 100 feet when there is no support. If wooden props are placed at 5 foot centers in row, and if the weight of the roof is equal to 5 pounds per square inch foot, then the load per prop is equal to 25 x 5 X 144x 5:90.00 pounds Hence,Y the cross sectional area for each prop is equal to 90,000 divided by 1000 or 90 squareinches, which is equivalent to a diameter of about 11.5 inches.

As a further example, assume that in the model, two beds failed when the span was equal to alprototype span of 400 Yfeet. The beds were 5 feet and 20 feet in thickness respectively. Hence, if it is desired to keep a span of 200y feet or more free from support, the propping must be designed for both rockV beds. For spans between 50 and 200 feet, only .the rst beds need be supported by artificial props. The load per prop supporting both rock beds at 5 foot centers will be equal to 25 25 5 144=450,000 lbs. Therefore, the cross sectional area of each prop is equal to 450,000 divided by 1000 or 450 equare inches which is equal to a diameter of about 24 inches.

Photoelastic procedure for the determirmtion'of the position of new openings with reference to previous openings and supports The general procedurefor testing` modelsrof; photoelastic materials is followed. The new openings may be placed in a model and in accordance with a scale previously decided upon. The model is then loaded by placing -it in a centrifuge and photographs of e the isochromatic fringes, of the isoclinic fringes'a'nd of the isopachic fringes are then obtained with suitable apparatus. `From these photographs, the contours of the principal stresses for the models are drawn and from these drawings the stress values and their directions at all points inthe prototype are determined. v f

Another photoelastic model with new openings placed at different points produces another stress diagram which may be compared with the one obtained with the first model. Thus, conclusions may be drawn as to the most desirable'place at Which new openings may be `placedI in Vorder to avoid areas of `high stress intensity. The position of new openings .with respect to present openings and pillars may therefore-be determined by this simple procedure which furnishes'information on stress changes that take place, the possibilities of failure, and necessity for support.

Although the position of newopenings with reference to previous openings and supports is preferably ascertained dynamically, for purposes of'iapproximations in` preparing the dynamic Wphotoelas'ti'c model;` advantage 'may 'be taken of static loading. e For photoelastic models built to scaleiand statically loaded, the following relationships hold:

S1, Tb

To iliustrate, if the total load on the prototyp which is concentrated on a pillar is known, and it is desired to construct a tunnel directly beneath the pillar, then, assuming that in a photoelastic model of the prototype, a rectangular Bakelite pillar has the following dimensions:

width, b :0.253 inch depth, Tb=0.305 inch and if the uniform pressure p, exerted by the pillar on the oor=735 lbs. per square inch, and M. R.=480

Y l Distance from center of tunnelto floor Y Phot-oelastic procedure for the determinationfof high stress areas or areas that are liable to failure and to rock bursts The procedurelast described for the determination of the position of new openings with reference to previous openings and supports by dynamic testing should be followed. Statica-Hy loaded models may be used for the purpose of making approximations,

The areas which ordinarily are subject to rock bursts are those having one or more free faces; those in hard rocks with high compressive strength and negligible viscous or plastic properties; those under high stress conditions; and those likely to have stresses increased considerably during a short or long period of time. A

The determination of the principal stresses and the, direction of the stresses before and after openings are made in proximity to high stress areas will present suiiicient data to give information on Whether the results will tend to a bursting of rock toward an opening or not. The values of these stressesin comparison with the physicalproperties of the geologic material willsupply A Tunnel diameter= 10.00 ft.

the answers to the problem. Materialsv with properties of quartzes, granites and the like, will' tend to burst; clays and plastic materials will tend' to flow.

Procedure for the prevention and control of burstsv The procedure previously outlinedy for the determination of the position of new openings is used. With' this information in mind, the openings are'so placed as to avoid high stressl concentration areas. If this procedure is inadvisable the following procedure may be used:

From the principal stress diagram,` determine the direction from which the burst is liable to come. Provide a cushion for the burst to expend itself upon, either by under cutting or by over cutting the ore body or coal vein and then blasting only a portion thereof so that should a burst occur thereafter, there would still be several feet ofj material to cushion it or absorb the shock; or, where cutting is not feasible, two long holes are drilled and two charges are placed therein, a charge in the rst half of the hole to'break out the material, anda charge in the second half or at the end of the hole to crack the remainder and to provide a cushion of broken material to absorb the shock of the burst. The possibilities of bursts may therefore be determined from a study of the fphysical characterists of the geologic material and from 'a determination of the principal stresses and their direction of action', especially in the regions where work is carried on or where openings are kept open for haulage and the like.

Thus, the effects of rock bursts may be minimized or overcome by protecting all the openings or working places where these are liable to occur, with a cushion or medium to absorb the shock. The media suggested are solid coal or ore or rock when overcutting or undercutting and shattered coal or ore or rock produced by longvhole drilling.

Time effects for plastic materials A great many of our geological materials are plastic, that is to say, have low elastic ranges.

They deform continuously with load and time, and have important effects on mining operations. To illustrate, the following have been noted:

1. The heaving of bottom or floors of openings tends to close them due to the plastic property of the bottom.

2. The plastic properties of the pillars themselves where a hardbottom and roof are present will now be considered. In such cases, a certain .underweight must move down with the pillar. l This results in throwing the load of a large span Block caving The procedure for the determination of whether portions of an ore body can be caused to break of their own accord because ofl gravitational forces and the time in which portions of `an ore body can be caused to break of their own accord because of gravitational forces, to a size suitable for handling in chutes and cars or in conveyers, and the development and procedure to be followed that will cause this to take place is illustrated in the following example: p

A modelV is constructed according to the-steps setV forth hereinbefore anda span of 2 inches by 1A inch high is mined out of the model'. If the scale assumed' is 1:1000 and if the oreI body is 167 feet thick, the model thickness will be about 2 inches. y y

If failure of the model occursb'efore thespeed equivalent to a model ratio of 1:1000 is reached, the fact is noted but` the test is run at a speed equivalent to a model ratio of 1:1000 nevertheless. The caved-in material is removed,'weigh'ed and screened and the percentageY of fines present under a predetermined size and the percentage of the block volume broken will bedetermined. This -will' be an indication of the block caving effects. If complete failure occurred, another model is :prepared with the span reduced to l inch. The test is repeated and similar data are obtained'.

Several models may be thus tested. With these data, a curve may be drawn by plotting model or prototype span against percentages of nes or percentages of volume broken. From this curve, one maybe able to choose the dimensions for caving blocks. By way of examplefif a one inc hspan in the scale model gave results best approximating the de siderata, the width of the span in the prototype would be equal to or 83 feet, and the height ofthe ore to be caved would be equal to or 16'? feet; lThe length of block could be anything in excess of 2x83 or 167 feet, and the longer, the better.

The dimensions of a block with a square cross section in plan, may be obtained if the previous results are multiplied by 2, that is to say, the prototype dimensions should be 2X 83 or 167 feet by 167 feet by 167 feet.

It must be noted, that. the complete height of ore is to be caved-in in one operation whenever possible unless it is composed of layers of strong and weak ores. In this latter case, thestrong layers may be weakened b-y development work, that is to say, the area at the shear sections is reduced by openings made particularly in the strong portions. The condition in which the complete height of ore body and overburden should not be caved-in in one operation is one in which the overburden will support itself over greater horizontal dimensions than that desired for the block, or one in which the overburden, though weak, is not thick enough to take up the space made by withdrawing a caving block or able to furnish the side pressure necessary to help in the breaking of the surrounding blocks.

In block caving, the load is applied when the supporting pillars of a block are removed. These may be removed suddenly or slowly. The effect of bringing the model up to speed amounts to the uniform removal of support in the eld with time effects that may be approximated.

effects maybe u sed to control block caving and thereby increase safety underground This relationship has already been discussed.

A Tests on the overlying materialY should now be made to determine minimum failure spans. It these spans are smaller than those determined for the ore, the block dimension for cavingshould be decreased and advantageY taken of the overweight. If thse spans areV equal to those for the ore, they may be included in the ore model tests. If greater, dimensions may be chosen to-give. the best caving effects on ore or that will permit overburden to cave with. it,

@and/or such, that tailings from the mill may be deposited 4on the surface over caving blocks or through bore holes in the caving ore, so that, when adjoining blocks are caved, the side pressure exerted alongside a block by caved overburden may be used.

Although the present invention has been described in conjunction with preferred embodiments, it is to be understood that modications and variations maybe resorted to'without departing from thespirit and scope of the invention, as those skilled in the art will readily'understand. Such variations' and modifications are considered to be .within the purview and 4scope of the appended claimsf forces and strains in the inverse ratio of model size to mine size to simulate field conditions, obtaining data from said testing on the relationship between the time required for failure of the scale models and the variable dimension, determining the time required for failure of equivalent mine structures in the iield from these test data in accordance with the principle that the time required for a given event to take place in a mine structure in the Vfield stressed beyond its elastic limit is equal to the product of the model scale multiplied by the time re- .The eiiect of increasing speed rapidly, that is to-say, obtaining the effect of an impact load, ,may also be studied and observed. These time jquired for the same event to take place vin the collapsed material of desired size which comprises studying the geologic section of a mine structure, obtaining representative field samples of the mine structure, obtaining data on the physical properties of the field samples, preparing scale models of the mine structure iri which 4a dimension of the mine structure is varied, Ysaid scale models being made in every respect of the same material as the prototype, testing the scale models in a centrifugal machine until portionsof each model collapse by imposing on, the model simulated gravitational forces 4and strains in the inverse ratio of model size to mine sizer to simulate field conditions,'obtaining data on the size distribution of the collapsed portions of each scale model by screening to ascertain the percentage of material below a desired size, determining the relationship between the percentage of material below the desiredsize in the collapsed portions and the variable dimension of the scale models, and designing the mine structure with that dimension which causes portions of said structure to collapse to the desired size in accordance with this relationship.

3. 'I'he method of mine designing to obtain a desired volume of collapsed material which comprises studying the geologic section of a mine structure, obtaining Yrepresentative iield samples -of the mine structure, obtaining data on the physicalY properties of the field samples, preparing scale models of the mine structure in which a dimension of the mine structure is varied. said scalemodels being madev inV every respect -oiV the same'material as the prototype, testing the scale models in a centrifugal machine until portions vof each model collapse by imposing on the model simulated gravitational forces and strains in the inverse ratio of model size to mine size to simulate iield conditions, obtaining data on the volume of material collapsed in each scale model; determining the relationship between volume of material collapsed and the variable dimension of the scale models, and designing the mine structure with that dimension kwhich causes the desired volume of said structure to collapse in accordance with this relationship. l

l PHILIRB. BUCK y. 

